Geometry and the Exceptional Jordan Algebra
Azimuth 2026-03-27
I’m giving a talk online tomorrow at the 2026 Spring Southeastern Sectional Meeting of the American Mathematical Society, in the Special Session on Non-Associative Rings and Algebras. The organizers are Layla Sorkatti and Kenneth Price. I doubt the talk will be recorded, but here are my slides:
• Projective geometry and the exceptional Jordan algebra.
Abstract. Dubois-Violette and Todorov noticed that the gauge group of the Standard Model of particle physics is the intersection of two maximal subgroups of
which is the automorphism group of the exceptional Jordan algebra
Here we conjecture that these can be taken to be any subgroups preserving copies of
and
that intersect in a copy of
Given this, we show that the Standard Model gauge group consists of all isometries of the octonionic projective plane that preserve an octonionic projective line and a complex projective plane intersecting in a complex projective line. This is joint work with Paul Schwahn.
This is an introductory talk for mathematicians. Physicists may prefer the two talks here. Those go much further in some ways, but they don’t cover the new ideas that Paul Schwahn and I are in the midst of working on.